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Question : If $(2x - 5y)^3 - (2x+5y)^3 = y[Ax^2 + By^2]$, then what is the value of $(2A - B)$?
Option 1: 25
Option 2: 10
Option 3: 15
Option 4: 40
Correct Answer: 10
Solution : According to the question, $(2x - 5y)^3 - (2x+5y)^3 = y[Ax^2 + By^2]$ ⇒ $[2x - 5y - 2x - 5y][4x^{2} + 25y^{2} + 20 xy + 4x^{2} - 25y^{2}] = y[Ax^{2} + By^{2}]$ ⇒ $[-10y] [ 12x^{2} + 25y^{2}] = y[Ax^{2} + By^{2}]$ ⇒
Question : A girl, walking at $\frac{5}{6}$ of her usual speed, misses the bus by 7 minutes. How long does it usually take to reach the bus stop?
Option 1: 24 minutes
Option 2: 35 minutes
Option 3: 30 minutes
Option 4: 60 minutes
Correct Answer: 35 minutes
Solution : Given, A girl, walking at $\frac56$ of her usual speed, misses the bus by 7 minutes. We know, Distance covered = speed × time taken Let the usual speed and usual time to reach the bus be $v$ and $t$, respectively. ⇒ The distance
Question : Comprehension:
In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank.
The modern pizza was originally (1).___________ in Naples, Italy but the word pizza is Greek in (2).___________ derived from the Greek word pktos meaning solid or clotted. The ancient (3).____________ covered their bread with oils, herbs and cheese. The first major (4).__________ that led to flatbread pizza was the use of tomato as a topping. It was common for the poor of the area around Naples to add (5).__________ to their yeast-based flat bread, and so the pizza began. Question: Select the most appropriate option to fill in the blank No. 2.
Option 1: align
Option 2: bulletin
Option 3: origin
Option 4: villain
Correct Answer: origin
Solution : The correct choice is the third option.
Origin means a point or place from where something arises, which in this context is the word "pizza". This helps convey the intended meaning of the sentence.
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
He is one of (those who likes to help others).
(1) those persons who like to help others
(2) those who like to help the other
(3) those who like to help others
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
Solution : The correct option is the third option.
Here, "those who likes to help others" should be replaced with "those who like to help others". It maintains the subject-verb agreement. Here, one of those means that the person is among those who like to
Question : Which of the following reasons is responsible for lack of vegetation in the desserts ?
Option 1: heavy volume of sands.
Option 2: absence of B-horizon in soil
Option 3: high temperature
Option 4: lack of rainfall
Correct Answer: lack of rainfall
Solution : The correct answer is lack of rainfall.
Rainfall is the limiting factor for the vegetation in desert areas. Deserts have a maximum rainfall of less than 25 cm per year. Deserts are classified in two types- hot deserts and cold deserts. Examples of
Question : Directions: In the following question, find the odd letter cluster from the given alternatives.
Option 1: UVWX
Option 2: SRQP
Option 3: LKJI
Option 4: HGFE
Correct Answer: UVWX
Solution : Let's check the options – First option: UVWX; U + 1 = V; V + 1 = W; W + 1 = X Second option: SRQP; S – 1 = R; R – 1 = Q; Q – 1 = P Third option: LKJI; L
Question : Concerning value addition in the textile industry, knitting is followed by which procedure?
Option 1: Garment manufacture
Option 2: Spinning
Option 3: Fibre production
Option 4: Dyeing and finishing
Correct Answer: Dyeing and finishing
Solution : The correct option is dyeing and finishing.
In the textile industry, knitting is often followed by the procedure of dyeing. After the fabric is knitted, it undergoes dyeing to impart colour and enhance its aesthetic appeal. Dyeing is a crucial step
Question : If $\frac{x}{y}+\frac{y}{x}=1$ and $x+y=2$, then the value of $x^3+y^3$ is:
Option 1: 1
Option 2: 3
Option 3: 0
Option 4: 2
Correct Answer: 0
Solution : $\frac{x}{y}+\frac{y}{x}=1$ and $x+y=2$ $⇒\frac{x^2+y^2}{xy}=1$ $⇒{x^2+y^2}=xy$ ___(i) $x^3+y^3=(x+y)(x^2+y^2-xy)$ From (i), $⇒x^3+y^3=0$ Hence, the correct answer is 0.
Question : In a $\small\triangle P M N$, S is a point on PM that divides PM in the ratio of 5 : 7. The line segment ST is parallel to MN. If MN = 24 cm, then what is the length (in cm) of segment ST?
Option 1: 16
Option 2: 17
Option 3: 14
Option 4: 10
Solution : Given: $MN =24$ cm $PS: SM=5:7$ Let $PS = 5x$ and $SM=7x$ ⇒ $PM = 5x+7x=12x$ Applying the congruent triangle rule on $\small\triangle PMN$ and $\small\triangle PST$ ⇒ $\frac{ST}{PS}=\frac{MN}{PM}$ ⇒ $\frac{ST}{5x}=\frac{24}{12x}$ ⇒ $ST=\frac{2}{x}\times5x$ $\therefore ST=10$ cm Hence, the correct answer is 10.
Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at 1, 2 and 3 that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).
Even though she was disliked by her in-laws at the beginning of her marriage, she did manage to win their hearts.
(1) win over their
(2) win over there
(3) win them over their
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 4
Solution : The correct answer is the fourth option.
"Win their hearts" implies that she made efforts to establish a positive and loving relationship with her in-laws, and she succeeded in doing so.
Therefore, the given sentence requires no improvement.
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